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Proceedings Paper

Defining the measurand in radius of curvature measurements
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Paper Abstract

Traceable radius of curvature measurements are critical for precision optics manufacture. An optical bench measurement of radius is very repeatable and is the preferred method for low-uncertainty applications. On an optical bench, the displacement of the optic is measured as it is moved between the cat's eye and confocal positions, each identified using a figure measuring interferometer. Traceability requires connection to a basic unit (the meter, here) in addition to a defensible uncertainty analysis, and the identification and proper propagation of all uncertainty sources in this measurement is challenging. Recent work has focused on identifying all uncertainty contributions; measurement biases have been approximately taken into account and uncertainties combined in an RSS sense for a final measurement estimate and uncertainty. In this paper we report on a new mathematical definition of the radius measurand, which is a single function that depends on all uncertainty sources, such as error motions, alignment uncertainty, displacement gauge uncertainty, etc. The method is based on a homogeneous transformation matrix (HTM) formalism, and intrinsically defines an unbiased estimate for radius, providing a single mathematical expression for uncertainty propagation through a Taylor-series expansion.

Paper Details

Date Published: 20 November 2003
PDF: 12 pages
Proc. SPIE 5190, Recent Developments in Traceable Dimensional Measurements II, (20 November 2003); doi: 10.1117/12.504884
Show Author Affiliations
Angela Davies, Univ. of North Carolina at Charlotte (United States)
Tony L. Schmitz, Univ. of Florida (United States)

Published in SPIE Proceedings Vol. 5190:
Recent Developments in Traceable Dimensional Measurements II
Jennifer E. Decker; Nicholas Brown, Editor(s)

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